The operational modal analysis methods based on output-only measurements are well-known and applied in linear systems. However, they are not so well developed for nonlinear systems. Thus, this paper proposes an approach for nonlinear system identification using output-only data. In the conventional Volterra series, the outputs of the system are computed by multiple convolutions between the excitation force and the Volterra kernels. However, in this paper at least two time series measured in different placements are used to compute the multiple convolutions and the excitation signals are not required. The novel kernels identified can be used to characterize nonlinear behavior through a model using only output data. A numerical example based on a Duffing oscillator with two degrees-of-freedom (2DOF) and experimental vibration data from a buckled beam with hardening nonlinearities are used to illustrate the proposed method. The prediction results using output-only data are similar to the conventional Volterra kernels based on input and output data.

The frequency range of the leak noise in buried water pipes, measured using acoustic correlators, depends significantly on the type of pipe and its location as well as the type of sensors used. Having a rough idea of this frequency range can be beneficial for operators prior to conducting tests; however, there is currently no method of predicting it except through practical experience, and no model-based approach yet exists. This issue is addressed in the present paper by using a concise and relatively simple analytical model of the water-pipe–soil system combined with the sensors’ frequency response. The influence of the various physical parameters of the system, such as the pipe and soil properties and the sensor type, on the cross-power spectral density (CPSD) of leak noise signals and, furthermore, the frequency range are investigated. The main factors that affect the bandwidth are the distance between the sensors, wave speed of the predominantly fluid-borne wave in the pipe and the attenuation of this wave. It is shown that the external medium has a profound effect on the propagation and, in turn, on the bandwidth. The approach to predicting this bandwidth is validated using experimental data from three different test sites.

Leak noise correlators are commonly used to detect and locate leaks in buried water pipes. They use the cross-correlation function between leak noise signals measured using hydrophones or accelerometers placed on the pipe either side of the leak. The efficacy of a correlator is dependent upon knowledge of the speed at which the leak noise propagates along the pipe as well as how much it attenuates with distance. The leak noise is carried in a predominantly fluid-borne wave in the pipe, which is heavily influenced by the pipe and soil properties. Although the pipe properties can be determined relatively easily, estimation of the soil properties surrounding the pipe is more problematic. It is desirable to have an accurate estimate of the soil properties, so that current models can be developed and used to improve understanding of leak noise propagation and hence leak detection capabilities. In this paper a novel approach to determining the bulk and shear moduli of the soil from measurements of the predominantly fluid-borne wave in a buried plastic pipe, is described. The measured data are compared with corresponding data predicted from a model, and the soil properties are determined using an optimization algorithm. The method is applied to two different sites, one in the UK, where the soil properties surrounding the pipe are representative of sandy soil, and one in Brazil, where the surrounding soil has properties that are representative of clay soil. It is found that the bulk and shear modulus can be estimated in the pipe buried in sandy soil, but in the clay soil it is only possible to estimate the shear modulus.

An appropriate model of leak noise at source is necessary in analytical and numerical approaches to investigate the characteristics of leak noise measured remotely from the leak in buried water pipes. It is extremely difficult to measure leak noise at source in practice, so an inverse method is needed to predict this from measurements made either side of the leak at convenient access points. This paper presents such a method, and illustrates the approach using four data sets from three different test sites. The method requires that the noise propagates in the pipe according to a simple model of wave propagation within the frequency range over which leak noise is detected at the sensors.Using the measured data, the real and imaginary parts of the wavenumber are estimated, and these, together with an estimated position of the leak between the two sensors, the frequency response functions corresponding to the sections of the pipe either side of the leak position are estimated. If pressure measurements are made, then both the level and shape of the leak noise spectrum can be estimated, but if accelerometers are used then only an estimate of the shape of the spectrum is possible. From the measurements presented, it is found that it is not possible to state categorically that the leak noise spectra decays according to a particular frequency power law. There is some evidence that it decays with a frequency power law of 1 ω − , which agrees with previous laboratory based experiments, but this is not definitive in all cases.

Nonlinear effects are broadly presents in several kinds of mechanical systems. Thus, it is necessary to use a suitable tool that becomes possible to characterize these nonlinearities in many situations. Volterra series can be useful for describing nonlinear systems through multiple convolutions. In this sense, the main goal of this work is to approximate the solutions of the motion equations using Volterra series in order to describe the nonlinear dynamical behavior of some mechanical benchmarks. Duffing oscillator, bilinear oscillator and a quadratically damped oscillator are analyzed to illustrate the efficiency, advantages and drawbacks of the proposed approach.

to describe a prediction of vibrating systems in nonlinear regime of motion.

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